Both tasks take as input the raw image and a binary mask representing a candidate object.

We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs that depend exclusively on the domain geometry, we design Neural Green's Function to imitate their behavior, achieving superior generalization across diverse irregular geometries and source and boundary functions. Specifically, Neural Green's Function extracts per-point features from a volumetric point cloud representing the problem domain and uses them to predict a decomposition of the solution operator, which is subsequently applied to evaluate solutions via numerical integration. Unlike recent learning-based solution operators, which often struggle to generalize to unseen source or boundary functions, our framework is, by design, agnostic to the specific functions used during training, enabling robust and efficient generalization. In the steady-state thermal analysis of mechanical part geometries from the MCB dataset, Neural Green's Function outperforms state-of-the-art neural operators, achieving an average error reduction of 13.9\% across five shape categories, while being up to 350 times faster than a numerical solver that requires computationally expensive meshing.

Incremental brain tumor segmentation is critical for models that must adapt to evolving clinical datasets without retraining on all prior data. However, catastrophic forgetting, where models lose previously acquired knowledge, remains a major obstacle. Recent incremental learning frameworks with knowledge distillation partially mitigate forgetting but rely heavily on generative replay or auxiliary storage. Meanwhile, diffusion models have proven effective for refining tumor segmentations, but have not been explored in incremental learning contexts. We propose Synthetic Error Replay Diffusion (SER-Diff), the first framework that unifies diffusion-based refinement with incremental learning. SER-Diff leverages a frozen teacher diffusion model to generate synthetic error maps from past tasks, which are replayed during training on new tasks. A dual-loss formulation combining Dice loss for new data and knowledge distillation loss for replayed errors ensures both adaptability and retention. Experiments on BraTS2020, BraTS2021, and BraTS2023 demonstrate that SER-Diff consistently outperforms prior methods. It achieves the highest Dice scores of 95.8\%, 94.9\%, and 94.6\%, along with the lowest HD95 values of 4.4 mm, 4.7 mm, and 4.9 mm, respectively. These results indicate that SER-Diff not only mitigates catastrophic forgetting but also delivers more accurate and anatomically coherent segmentations across evolving datasets.

We proposed a novel test-time optimisation (TTO) approach framed by a NeRF-based architecture for long-term 3D point tracking. Most current methods in point tracking struggle to obtain consistent motion or are limited to 2D motion. TTO approaches frame the solution for long-term tracking as optimising a function that aggregates correspondences from other specialised state-of-the-art methods. Unlike the state-of-the-art on TTO, we propose parametrising such a function with our new invertible Neural Radiance Field (InvNeRF) architecture to perform both 2D and 3D tracking in surgical scenarios. Our approach allows us to exploit the advantages of a rendering-based approach by supervising the reprojection of pixel correspondences. It adapts strategies from recent rendering-based methods to obtain a bidirectional deformable-canonical mapping, to efficiently handle a defined workspace, and to guide the rays' density. It also presents our multi-scale HexPlanes for fast inference and a new algorithm for efficient pixel sampling and convergence criteria. We present results in the STIR and SCARE datasets, for evaluating point tracking and testing the integration of kinematic data in our pipeline, respectively. In 2D point tracking, our approach surpasses the precision and accuracy of the TTO state-of-the-art methods by nearly 50% on average precision, while competing with other approaches. In 3D point tracking, this is the first TTO approach, surpassing feed-forward methods while incorporating the benefits of a deformable NeRF-based reconstruction.

Neural Information Processing Systems http://nips.cc/

Deep neural networks (DNNs) are increasingly used to solve partial differential equations (PDEs) that naturally arise while modeling a wide range of systems and physical phenomena. However, the accuracy of such DNNs decreases as the PDE complexity increases and they also suffer from spectral bias as they tend to learn the low-frequency solution characteristics. To address these issues, we introduce Parametric Grid Convolutional Attention Networks (PGCANs) that can solve PDE systems without leveraging any labeled data in the domain. The main idea of PGCAN is to parameterize the input space with a grid-based encoder whose parameters are connected to the output via a DNN decoder that leverages attention to prioritize feature training. Our encoder provides a localized learning ability and uses convolution layers to avoid overfitting and improve information propagation rate from the boundaries to the interior of the domain. We test the performance of PGCAN on a wide range of PDE systems and show that it effectively addresses spectral bias and provides more accurate solutions compared to competing methods.

MRI reconstruction techniques based on deep learning have led to unprecedented reconstruction quality especially in highly accelerated settings. However, deep learning techniques are also known to fail unexpectedly and hallucinate structures. This is particularly problematic if reconstructions are directly used for downstream tasks such as real-time treatment guidance or automated extraction of clinical paramters (e.g. via segmentation). Well-calibrated uncertainty quantification will be a key ingredient for safe use of this technology in clinical practice. In this paper we propose a novel probabilistic reconstruction technique (PHiRec) building on the idea of conditional hierarchical variational autoencoders. We demonstrate that our proposed method produces high-quality reconstructions as well as uncertainty quantification that is substantially better calibrated than several strong baselines. We furthermore demonstrate how uncertainties arising in the MR econstruction can be propagated to a downstream segmentation task, and show that PHiRec also allows well-calibrated estimation of segmentation uncertainties that originated in the MR reconstruction process.

The application of compressed sensing (CS)-enabled data reconstruction for accelerating magnetic resonance imaging (MRI) remains a challenging problem. This is due to the fact that the information lost in k-space from the acceleration mask makes it difficult to reconstruct an image similar to the quality of a fully sampled image. Multiple deep learning-based structures have been proposed for MRI reconstruction using CS, both in the k-space and image domains as well as using unrolled optimization methods. However, the drawback of these structures is that they are not fully utilizing the information from both domains (k-space and image). Herein, we propose a deep learning-based attention hybrid variational network that performs learning in both the k-space and image domain. We evaluate our method on a well-known open-source MRI dataset and a clinical MRI dataset of patients diagnosed with strokes from our institution to demonstrate the performance of our network. In addition to quantitative evaluation, we undertook a blinded comparison of image quality across networks performed by a subspecialty trained radiologist. Overall, we demonstrate that our network achieves a superior performance among others under multiple reconstruction tasks.